INTER TEMPORAL CHOICE

INTER-TEMPORAL CHOICE OF RATIONAL CONSUMER

BY EDE KENECHUKWU KENNETH edekenechukwuk@gmail.com

Inter-temporal choices are the choice a consumer makes considering two periods: period 1 (present period) and period 2 (future period). Irvin Fisher in his hypothesis of inter-temporal choices reasoned that people makes decision on how much to consume and how much to save. The more consumption today, brings less consumption tomorrow. This gave rise to enquires into inter temporal budget constraint. To discuss this model, there are certain assumptions:

1.  The consumer faces two periods namely; period 1 and period 2.

2.  Period 1 represents consumer youthful age, while period 2 represents consumer’s old age.

3.  The consumer consumes at C₁ and earn income Y₁ in period 1 and also earn income Y₂ and consumption C₂ in period 2.

4.  Since consumer can borrow his consume could be ≤ or ≥ income in that period.

5.  The consumer saving in period1 is S=Y₁ – C₁ and his consumption in period2 is C₂ = Y₂+ (I + r) S.

6.  Saving S represents borrowing or saves since the consumer can save or borrow. Then we have the equation below as consumer budget constraint.

C₂ = Y₂ + (I+r) (Y₁- C₁)

C₂ = Y₂ + (I+r) Y1 – (I+r) C1

C₂+ (I+r) C₁ = Y2 + (I+r) Y₁

Divide both sides with I+r (I+r)

C2 + (I+r) C1     =       Y2 + (I+r) Y1

   I+r (I+r)                         I+r (I+r)

C2+C1      =     Y2 + Y1

  (I+r)                  (I+r)

We shall explain better with the curve below:

The equation shows the standard way of expressing consumers inter- temporal choices. If the interest rate is equal to zero, then the total consumption in period1 equals the total consumption in period2. But if the interest rate is greater than zero, the future consumption and income are discounted by a factor (I+r). This arises from interest earned on savings. Because of interest earned on current income, future income is worth less than the current income. 1/(I+r) is the factor price paid for period2. Consumption measured in terms of period1.